Why is comparing models based on likelihood acceptable?

by badmax   Last Updated September 12, 2018 14:19 PM

Suppose for instance I have a set of models and I want to choose the best one. One way I've seen is to use something like AIC or BIC. I'm not sure how higher likelihood translates into a better model - I can create a model that assigns probability 1 to my data set and 0 everywhere else under whatever parameters I want. Clearly this is pathological but I'm pretty sure with enough tries I can create a model that assigns whatever likelihood I want.

Why then is likelihood based evaluation on non-nested models acceptable?

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